Evaluate 9x-7y>3(3x-7z)

$9 x - 7 y > 3 (3 x - 7 z)$

Step 1

Simplify $3 (3 x - 7 z)$ .

Rewrite.

$9 x - 7 y > 0 + 0 + 3 (3 x - 7 z)$

Simplify by adding zeros.

$9 x - 7 y > 3 (3 x - 7 z)$

Apply the distributive property.

$9 x - 7 y > 3 (3 x) + 3 (- 7 z)$

Multiply.

Multiply $3$ by $3$ .

$9 x - 7 y > 9 x + 3 (- 7 z)$

Multiply $- 7$ by $3$ .

$9 x - 7 y > 9 x - 21 z$

Step 2

Move all terms containing $x$ to the left side of the inequality.

Subtract $9 x$ from both sides of the inequality.

$9 x - 7 y - 9 x > - 21 z$

Combine the opposite terms in $9 x - 7 y - 9 x$ .

Subtract $9 x$ from $9 x$ .

$- 7 y + 0 > - 21 z$

Add $- 7 y$ and $0$ .

$- 7 y > - 21 z$

Step 3

Divide each term in $- 7 y > - 21 z$ by $- 7$ and simplify.

Divide each term in $- 7 y > - 21 z$ by $- 7$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 7 y}{- 7} < \frac{- 21 z}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 y}{- 7} < \frac{- 21 z}{- 7}$

Divide $y$ by $1$ .

$y < \frac{- 21 z}{- 7}$

Simplify the right side.

Cancel the common factor of $- 21$ and $- 7$ .

Factor $- 7$ out of $- 21 z$ .

$y < \frac{- 7 (3 z)}{- 7}$

Cancel the common factors.

Factor $- 7$ out of $- 7$ .

$y < \frac{- 7 (3 z)}{- 7 (1)}$

Cancel the common factor.

$y < \frac{- 7 (3 z)}{- 7 \cdot 1}$

Rewrite the expression.

$y < \frac{3 z}{1}$

Divide $3 z$ by $1$ .

$y < 3 z$

Step 4

The variable $x$ got canceled.

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$

Evaluate 9x-7y>3(3x-7z)

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